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Fuzzy Goal Programming Approach to Quadratic Bi-Level Multi-Objective Programming Problem

by Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 29 - Number 6
Year of Publication: 2011
Authors: Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri
10.5120/3571-4926

Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri . Fuzzy Goal Programming Approach to Quadratic Bi-Level Multi-Objective Programming Problem. International Journal of Computer Applications. 29, 6 ( September 2011), 9-14. DOI=10.5120/3571-4926

@article{ 10.5120/3571-4926,
author = { Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri },
title = { Fuzzy Goal Programming Approach to Quadratic Bi-Level Multi-Objective Programming Problem },
journal = { International Journal of Computer Applications },
issue_date = { September 2011 },
volume = { 29 },
number = { 6 },
month = { September },
year = { 2011 },
issn = { 0975-8887 },
pages = { 9-14 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume29/number6/3571-4926/ },
doi = { 10.5120/3571-4926 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:15:03.619940+05:30
%A Surapati Pramanik
%A Partha Pratim Dey
%A Bibhas C. Giri
%T Fuzzy Goal Programming Approach to Quadratic Bi-Level Multi-Objective Programming Problem
%J International Journal of Computer Applications
%@ 0975-8887
%V 29
%N 6
%P 9-14
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper deals with fuzzy goal programming approach to quadratic bi-level multi-objective programming problem involving a single decision maker with multiple objectives at the upper level and a single decision maker with multiple objectives at the lower level. The objective functions of each level decision maker are quadratic in nature and the system constraints are linear functions. In the model formulation of the problem, we first determine the individual best solution of the quadratic objective functions subject to the system constraints and construct the quadratic membership functions of the objective functions of both levels. The quadratic membership functions are then transformed into equivalent linear membership functions by first order Taylor series at the individual best solution point. A possible relaxation of each level decision is considered by providing preference bounds on the decision variables for avoiding decision deadlock. Fuzzy goal programming approach is then used to achieve maximum degree of each of the membership goals by minimizing negative deviational variables. To demonstrate the efficiency of the proposed approach, an illustrative numerical example is provided.

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Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy goal programming Quadratic programming Quadratic bi-level programming Quadratic bi-level multi-objective programming

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